Two vertical poles 20m and 30m high are 60m apart.A rope is to be attached from the top of one pole to a point on the ground halfway between the poles and then to the top of the other pole.How long a rope is needed?
one triangle is 20 by 30
the other is 30 by 30
sqrt(30^2+30^2) + sqrt(20^2+30^2)
To find the length of the rope needed, we can use the Pythagorean theorem.
Let's label the vertical poles as pole 1 (20m high) and pole 2 (30m high). The distance between the poles is 60m.
First, we need to find the distance from the top of pole 1 to the halfway point on the ground between the poles. Since the distance between the poles is 60m, the halfway point is at a distance of 60/2 = 30m from pole 1.
Using the Pythagorean theorem, we can find the distance from the top of pole 1 to the halfway point:
distance^2 = (30m)^2 + (20m)^2
distance^2 = 900m^2 + 400m^2
distance^2 = 1300m^2
Now, let's find the distance from the halfway point to the top of pole 2. Since pole 2 is 30m high, the total length needed is 30m.
Finally, we can find the total length of the rope needed by adding the two distances:
total length = distance + pole 2 height
total length = √(1300m^2) + 30m
total length ≈ 36.06m
Therefore, a rope of approximately 36.06 meters is needed.
To find the length of the rope needed, we can use the Pythagorean theorem. Here's how:
1. Draw a diagram to visualize the given information. Let's call the poles A and B, with heights 20m and 30m respectively. The distance between the poles is 60m.
A ------ 60m ------- B
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2. We can see that the rope will form a right-angled triangle with poles A and B. Let's call the point at the ground halfway between the poles as C. The rope will be attached from A to C and then from C to B.
A ------ 60m ------- B
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---C-----
3. Since C is the midpoint of the distance between the poles, the distance from C to either A or B will be half of the distance between the poles, which is 60m/2 = 30m.
4. Now we have a right-angled triangle with sides AC, BC, and AB, where AC = BC = 30m. We need to find AB, which represents the length of the rope.
5. Apply the Pythagorean theorem: The square of the hypotenuse (AB) is equal to the sum of the squares of the other two sides (AC, BC).
AB^2 = AC^2 + BC^2
AB^2 = 30^2 + 30^2
AB^2 = 900 + 900
AB^2 = 1800
6. Take the square root of both sides to find the length of AB (the rope):
AB = √(1800)
≈ 42.43m
Therefore, the length of the rope needed is approximately 42.43 meters.